Potentially controversial answer
From what I remember being told (by a Japanese friend of mine), all of the Kana where invented by a single woman or a small group of women. I'm not sure on the validity of this, as it seems to be a hot topic with Japanese scholars.
As far as I'm aware, the Kana where both developed to aid in the study of Kanji. Since most kanji have multiple readings, it would make it easier for novice learners to remember the phonetic pronunciations of Kanji using a simple key.
PERSONAL OPINION SECTION STARTS HERE
I feel as though Hiragana uses shapes that are very similar to some elementary Kanji. Since Kunyomi readings seem to be the simpler ones to remember (your experience may differ), I'd say that shapes resembling the kanji where chosen for Hiragana for that purpose.
PERSONAL OPINION SECTION ENDS HERE
This might be why most systems use Katakan for onyomi readings and Hiragana for kunyomi readings - at least, that's how I view it.
Looking at most of the Hiragana characters, it's easy to see why women would have used them for writing, whereas Men would have used Katakana + Kanji (as has been pointed out by others)
The other thing to remember - as with most cultures - the skill of reading was usually taught to those who had the ability to pay to be taught (it was, usually seen as more of a privilege than a right, as it is these days). Thus, children who were born to families with the means to educate them, and the desire for them to reach high standing would pay for their children to study.
The consensus back then was that women had no place in the court, and the only place for someone who was educated was - you guessed it - at court. So, men would have be taught Kanji as part of their education in Chinese classics, Confucianism, Buddhism and history; whereas Women would have not have been taught such things.
I've no idea when, but at some point someone decided to invent a written script so that they could communicate - which is where the theory that it was a woman comes in. This implies that the person (or people) who invented the Kana where of high standing (otherwise they'd have to toil all day), and that they needed to communicate, in writing, with someone who was educated - probably a Husband or Father, due to the history of "Kidnapping" one's opponent's family members (again, this is speculation on my part).
this would also enable the Wives, Sisters and Mothers of the men of the court to educate eat other, and learn to read Kanji, This, in and of itself, would give rise to women being able to read and write - which gave rise to things like "The Tale of Genji".
I realise this answer is a little ramble-o-matic in nature, that I may have skated around the topic, and that I haven't quoted any sources (I'm at work at the minute, but I'll edit later on as and when I find evidence); so I apologise if this isn't of a high enough standard to answer the original question.